Wed Nov 5, 2014
234 Moses Hall, 6–8 PM
|Working Group in the History and Philosophy of Logic, Mathematics, and Science
Richard Zach (University of Calgary)
The Decision Problem and Logical Metatheory
The emergence of first-order logic and its metatheory is commonly seen as a switch from a purely axiomatic development of the logical systems in the Hilbert school to a metalogical view that incorporates model-theoretic methods. Although one origin of these model theoretic methods undoubtedly can be found in the work of Skolem and later Gödel and Tarski, to whom they are usually credited, even in the Hilbert school itself work on the decision problem independently gave rise to model-theoretic thinking, occasioned by the needs for proving decidability. The episode shows how mathematical practice can force fundamental changes in methodology.